There are a variety of mechanical positioning systems in use in the prior art for various purposes, and the common function and requirement of such systems is the accurate and repeatable positioning of a workpiece The majority of such positioning systems include a positional central platform or table to which the workpiece is mounted while the platform is in turn coupled to X-axis and Y-axis motors or drivers which move the platform or table along the corresponding X-axis or Y-axis X axis. Positioning errors occur, however, when the table or platform is moved from a first position to a second position and, depending upon the positioning accuracy required by the system, can be quite significant, thereby severely limiting the usefulness of such positioning systems.
Such positioning errors arise from a number of causes, the majority of which are based in the limitations of mechanical bearing, measuring and drive systems and are commonly referred to as Abbe errors. For the purposes of the present discussions, Abbe error may be defined as an error resulting where a measurement scale line does not intersect the viewing point of the subject of the measurement. In general, an Abbe error is proportional to the distance between the line of the measurement scale and the line of the viewpoint of the subject of the measurement. For example, the X-axis and Y-axis drives are typically separate motors or other mechanical driving devices and usually generate rotational motions that are turned into separate linear motions along the X- and Y-axis. In as much as it would be very unusual for two separate drive devices and their associated drive trains to be identical, there will be some error, such as small rotational errors of the drives, tolerances in the drive trains, frictional differences between the drive trains, and strictional losses, which will translate linear movement errors at the table or platform. As a result, such Abbe error(s) may, for example, result in the orientation of the repositioned table or platform becoming slightly skewed or misaligned by a small percentage of a degree or so. While such errors are typically small, and may cancel each other to an extent, the errors will still probably be significant in terms of the sought after accuracies in table movement and positioning, such as when the system is trying to control the movement of the table or platform to a new desired position as precisely as possible, e.g., within a half of a micron or so.